On Tuesday, Miami-Dade County Commissioners are likely to approve a plan to keep unwanted cats and dogs out of the county shelter’s death chamber, taking a giant step toward a goal that longtime pet rescuers thought they’d never see: a public shelter that more animals leave alive than in body bags.

The plan is Animal Services Department Director Alex Muñoz’s blueprint for achieving the “no kill’’ objective that the county commission adopted last July, defined as a 90 percent “save rate.’’

The vehicle to enable this breakthrough: an estimated $20 million budget boost from a property-tax increase that nearly 65 percent of voters — 500,000 — supported in a non-binding straw vote last November.

It would cost the average property owner $20 a year, or $10 for every $100,000 of value. Among other things, it would pay for more veterinarians and vet techs at Animal Services, more off-site adoption events, and keep a mobile clinic on the road seven days a week.

Nonprofits would be able to submit grant proposals for projects such as responsible pet-ownership education programs and rescuer stipends to an advisory board that would then make recommendations to the commission. The commission would decide which projects to fund.

A grassroots coalition called Pets Trust Miami campaigned to put the straw-ballot question before voters, then gave Muñoz its research. He included much of it in the plan that commissioners are expected to approve.

Pets Trust Miami is a nonprofit that got no public funding. It will not control the advisory board or decide who gets tax money.

The plan’s cornerstone is making free and low-cost spay/neuter widely available, to curb overpopulation and reduce the number of animals entering the shelter: up to 37,000 a year, many of them feral cats from a population estimated at more than 400,000.

But stripped from the plan is Muñoz’s and the Pets’ Trust plan to have several high-volume clinics that would have done nothing but spay/neuter in low-income areas where there are few veterinarians.

This happened after a lobbyist for the South Florida Veterinary Medical Association told commissioners at the June 12 Public Safety and Animal Services Committee meeting that his clients objected to the clinics.

At that session, only one commissioner objected to the plan: District 3’s Audrey Edmonson, who wondered why her colleagues are willing to raise taxes for animals while cutting human services like “affordable housing, services to the needy and poor children and elders.’’

But she said she’d ultimately support it because “the voters voted for it.’’

The vets’ lobbyist, Miguel Diaz de la Portilla, a member of the Florida senate and a former Miami-Dade County Commissioner, told the committee that Miami-Dade’s 167 veterinary hospitals would be able to handle extra sterilizations and that vets favor a voucher system.

Both the Muñoz and Pets Trust organizers figure that vets would need to perform at least 1,500 sterilizations weekly to keep the “no kill’’ goal on track.

Michael Rosenberg, Pets Trust co-founder, said it was great that the vets agreed to accept the responsibility, but he questioned whether most could handle the extra load or would willingly pass up lucrative private patients to work on voucher cases.

Diaz de la Portilla didn’t return several voicemails and emails.

Dr. Maria Oliveria, president of the South Florida Veterinary Medical Association, said in an email: “We will be working closely with ASD on the plan details and on the implementation of the new resolution when it passes. Unfortunately, I do not have further details for you at this time since things are still in the air about many details.’’

It’s unclear what a voucher would pay, but Miami-Dade Animal Services charges $30 for dogs and $15 for cats. Vets typically charge $300 to $600 for a dog sterilization.

Lauri Bloom, an attorney and animal activist, said that the specialty clinics, which were never envisioned as “bricks and mortar,’’ but pre-fab units, wouldn’t have competed with established vets because they’d be in underserved areas.

She said such a clinic would have made a huge difference in South Miami-Dade, a dumping ground for abandoned, often terrified pets that rescuers have to catch, cage, then transport to clinics on their own time and at their own expense.

“For me, the average trip is 45 minutes each way,’’ said Bloom, whose relatives ran the El Saba no-kill kennels in South Miami-Dade for 35 years.

Still, she was thrilled that the commission and the public were finally taking pet overpopulation seriously.

“Five years ago nobody cared and you couldn’t get a discussion going,’’ she said, crediting Pets Trust for kick-starting the issue. “This has shown the commissioners and politicians that constituents really care about this, so much so that [commissioners] have spent hours at meetings discussing it.

“Because of that, there will be fewer animals that will be suffering. It really is a cause for celebration.’’

Momentum has been building toward “no kill’’ since 2005, when for the first time, a veterinarian, Dr. Sara Pizano, took charge of the shelter and Animal Services became its own department, rather than a subsidiary of the police or public works departments.

Since then, the euthanasia rate has been dropping as adoptions, rescues, fostering and out-of-state relocations have climbed and the county put more emphasis on a trap/neuter/return program for feral cats.

Muñoz, who took over ASD in 2011, told the commission that so far this year, the dog “save rate’’ is nearly 80 percent, and cats are up to 60 percent. He said that the remaining dogs tend to be the least adoptable: large, dark-colored mutts.

Other upcoming and recent changes in animal care:

• A new county shelter is due to open in Doral in January 2014. Muñoz said it will house about 400 animals, include a triage suite and likely double the number of clinic examining tables to eight, enabling more sterilizations.

The antiquated shelter in Medley will close.

• The Miami-Dade School Board this year launched a K-8 curriculum during May’s Be Kind to Animals Week that stresses responsible pet ownership and the special role that pets play in family life. The hope is that children will take home what they’ve learned and educate their parents about proper pet care.

It curriculum grew out of school board member Dr. Martin Karp’s annual HOPE contest (Help Overcome Pet Euthanasia), a student essay/action plan competition in collaboration with Animal Services and the Humane Society of Greater Miami.

He launched it 20 years ago when, while he was teaching, he became aware of the grim situation at the county shelter, and decided the public needed to learn about conditions contributing to it.

“Now we have a lesson in three grade levels that relates to Common Core’’ State Standards in Language Arts, and Next Generation Sunshine State Standards in Science, he said.

• An anonymous benefactor gave Friends Forever Rescue, a nonprofit with a rented South Miami-Dade shelter, five acres near Monkey Jungle. Friends Forever founder Dee Chess said she’s working on zoning for air conditioned, hurricane-rated modular units that would house up to 200 dogs in a no-kill shelter/adoption facility.

“We already have volunteers waiting to sign up,’’ she said.

• The commission is considering measures to protect guard dogs and increase penalties for cruelty to horses.